For ED there is also the added difficulty that it is formulated most naturally in the Schrödinger representation, which has not proven to be the most convenient setting for demonstrating renormalizability in many quantum field theory applications. While one may conceive of first transforming to the Heisenberg or interaction pictures for computational purposes, such a transformation would technically require a well-defined \( \hat{T}_{\mu \nu }\)  to do so; nonetheless, an attempt in this direction for simple semi-classical models is given in [1]}, and for semi-classical gravity itself in [2]}. Other schemes based firmly in the Schrödinger representation have also been explored (see e.g., [3]}[4]}[5]}), but it would be rather misleading to suggest that the literature on this subject is nearly as rich as in the usual approaches.
